A right triangle with sides 1 and 2 has a hypotenuse equal to the square
root of 5, which is irrational - it carries on to infinity without
recurring - but the side length of a triangle must be finite!

Ravina wants to cut a square cake using straight vertical cuts to make
five pieces of equal volume. If she makes the first cut from the cake's
center to the top left corner, where must she make the other cuts if they
all start from the cake's center?

I'm trying to prove the formula that the area of a triangle with coordinates (0,0), (x1,y1), and (x2,y2) is 1/2(x1y2 - x2y1) without using determinants. Seems like I saw one years ago, but I can't recall it.

A figure shows a 12-foot ladder leaning across a 5-foot fence and
touching a higher wall located 3ft behind the fence. You want to find the
distance x from the base of the ladder to the bottom of the fence. . .

On a perfectly circular, small, flat island, a glass dome covers the
island, forming a perfect hemisphere. If the canopy is 10 feet tall at
the center of the island, how far from the center can 6-foot-tall Omar
walk upright?